Vol. 310, No. 2, 2021

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Decompositions of principal series representations of Iwahori–Hecke algebras for Kac–Moody groups over local fields

Auguste Hébert

Vol. 310 (2021), No. 2, 303–353
DOI: 10.2140/pjm.2021.310.303
Abstract

Recently, Iwahori–Hecke algebras were associated to Kac–Moody groups over non-Archimedean local fields. In a previous paper, we introduced principal series representations for these algebras and partially generalized Kato’s irreducibility criterion. Here, we study how some of these representations decompose when they are reducible and deduce information on the irreducible representations of these algebras.

Keywords
Kac–Moody groups, Iwahori–Hecke algebras, principal series representations, non-Archimedean local fields
Mathematical Subject Classification 2010
Primary: 20C08, 20G44
Secondary: 20E42, 22E50
Milestones
Received: 16 March 2020
Accepted: 15 December 2020
Published: 8 March 2021
Authors
Auguste Hébert
École normale supérieure de Lyon
Lyon
France